U.S. Pat. No. 4,472,880 describes a cutting machine with annular saw blade, which has an inner edge which is bevelled in a wedge-shaped manner, co-operating with a drive wheel inside the inner edge of the blade. The drive wheel consisted according to this patent of two halves which were pressed against each other in axial direction by a strong string. At the same time, the two halves of the drive wheel pressed the inner edge of the cutting blade between themselves, which gave a good grip but which also resulted in a hard wear. This design therefor was abandoned for an undivided drive wheel with a design disclosed in U.S. Pat. No. 4,793,065, FIG. 3. The grip between the inner edge of the saw blade and the drive wheel with its groove in this design is provided by the blade being pressed in a radial direction into a groove in the drive wheel. The wear thereby is reduced in comparison with the wear in the first embodiment according to U.S. Pat. No. 4,472,880 but is nevertheless substantial. Both the drive wheel and the saw blade are therefor to be considered as replacement parts which must be replaced when they have been worn out. The drive wheel in general certainly has a longer lifetime than the saw blade, but the costs for the exchange are nevertheless considerable. Nor is it beneficial from all parts of view that the saw blade and the drive wheel are replacement parts with substantially different lifetime, since this may increase the number of necessary replacement operations.